Answer
$$\begin{pmatrix}1&-1\\ -\frac{5}{2}&3\end{pmatrix}$$
Work Step by Step
We know the following equation for the inverse of a matrix:
$$\begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}$$
Thus:
$$\frac{1}{\det \begin{pmatrix}6&2\\ 5&2\end{pmatrix}}\begin{pmatrix}2&-2\\ -5&6\end{pmatrix} \\ \begin{pmatrix}1&-1\\ -\frac{5}{2}&3\end{pmatrix}$$
